TY - GEN

T1 - The geodesic diameter of polygonal domains

AU - Bae, Sang Won

AU - Korman, Matias

AU - Okamoto, Yoshio

PY - 2010

Y1 - 2010

N2 - This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n 7.73) or O(n 7 (logn + h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.

AB - This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n 7.73) or O(n 7 (logn + h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.

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U2 - 10.1007/978-3-642-15775-2_43

DO - 10.1007/978-3-642-15775-2_43

M3 - Conference contribution

AN - SCOPUS:78249234391

SN - 3642157742

SN - 9783642157745

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 500

EP - 511

BT - Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings

T2 - 18th Annual European Symposium on Algorithms, ESA 2010

Y2 - 6 September 2010 through 8 September 2010

ER -